Peyton needs to order some new supplies for the restaurant where she works. The restaurant needs at least 732 forks. There are currently 287 forks. If each sentence on sale contains 10 forks right and solve an inequality which can be used to determine X, The number of sets of forks Peyton could buy for the restaurant to have enough forks

Answer:

tn = n·a

 t10 = 10a

Step-by-step explanation:

We observe that the coefficient of 'a' is the term number:

 tn = n·a

 t10 = 10a

Step-by-step explanation:

The three functions that need to be ordered so that each one is Big-Oh of the next one are given below : log n2n4 log n nlog The correct order of these functions would be: nlog(n) << n^(1/2) << n^2 << n^(log(n)) << 2^n

Justification: To determine the order of these functions, let's first compare log n2 with n. As n tends to infinity, n increases much faster than log n2. Thus, n is the Big-Omega of log n2. We can write it as: log n2 = O(n).Next, let's compare n with 4 log n.

For large values of n, the term 4 log n is much smaller than n. Therefore, we can say:n = O(4 log n)Next, we need to compare 4 log n with nlogn. Using logarithmic identities, we can write 4 log n as log n^4. Now, let's compare this with nlogn:log n^4 = 4 log n = O(n log n)

Hence, we can say that 4 log n is Big-Oh of nlogn. Now, we need to compare nlogn with n^(logn). One way to compare these two functions is to take their ratio and see what happens as n tends to infinity: lim n→∞ (nlogn / n^(logn))= lim n→∞ (n^logn / n^(logn))= lim n→∞ n^0= 1

Thus, we can say that nlogn is Big-Oh of n^(logn).

Hence, the correct order of these functions is:log n2 << n << 4 log n << nlogn << n^(logn).

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The claim being tested is whether the proportion of men who own cats is smaller than 80% at a significance level of 0.10. A sample of 80 people is taken, and it is found that 74% of them own cats. To conduct the hypothesis test, the null and alternative hypotheses need to be stated, the type of test needs to be determined, the test statistic needs to be calculated, and the critical value needs to be determined.

(a) The null hypothesis (H0): The proportion of men who own cats is not smaller than 80%. The alternative hypothesis (Ha): The proportion of men who own cats is smaller than 80%.

(b) The type of test: This is a left-tailed test because the claim is that the proportion is smaller than the given value (80%).

(c) The test statistic: To test the claim about proportions, the z-test statistic is commonly used. In this case, the test statistic can be calculated using the formula:

  z = (q - p) / √(p(1 - p) / n)

where q is the sample proportion, p is the hypothesized proportion (80%), and n is the sample size.

(d) The critical value: The critical value for a left-tailed test at a significance level of 0.10 can be determined using a standard normal distribution table or a statistical software.

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The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

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For polynomial 1 the equation is binomial and by the degree its name is quadratic.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

For polynomial 1:

(x -1/2)(6x+2)

First simplifying the equation

6x² -3x +2x -1

6x² -x -1

thus, the equation is binomial and by the degree its name is quadratic.

For polynomial 2:

(7x^2+3x)-1/3(21x^2-12)

First simplifying the equation

+3x -(-4)

3x +4

thus, the equation is monomial and by the degree its name is linear.

For polynomial 3:

4(5x^2-9x+7)+2(-10x^2+18x-13)

First simplifying the equation

20x² -36x +28 - 20x² +36x -26

2

thus, the equation is constant and by the degree its name is linear.

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The relation R defined on N by (a, b) ∈ R if and only if b is greater than or equal to a, satisfies the properties of reflexive, transitive, and antisymmetric, but not symmetric.

To determine whether the relation R satisfies each of the properties, we can analyze its characteristics.

1. Reflexive: A relation R on a set A is reflexive if every element of A is related to itself. In this case, for every natural number a, (a, a) ∈ R because a is greater than or equal to itself. Therefore, R is reflexive.

2. Symmetric: A relation R on a set A is symmetric if for every pair (a, b) ∈ R, the pair (b, a) ∈ R as well. However, in the given relation R, if (a, b) ∈ R, it means that b is greater than or equal to a. But it does not imply that a is greater than or equal to b. Hence, R is not symmetric.

3. Antisymmetric: A relation R on a set A is antisymmetric if for every distinct pair (a, b) ∈ R, the pair (b, a) ∉ R. In the given relation R, if (a, b) ∈ R and (b, a) ∈ R, then a = b. Since a and b are distinct natural numbers, they cannot be equal. Therefore, R is antisymmetric.

4. Transitive: A relation R on a set A is transitive if for every triple (a, b) ∈ R and (b, c) ∈ R, the pair (a, c) ∈ R as well. In the given relation R, if (a, b) ∈ R and (b, c) ∈ R, then b is greater than or equal to a, and c is greater than or equal to b. Therefore, c is also greater than or equal to a, implying that (a, c) ∈ R. Hence, R is transitive.

In summary, the relation R defined on N by (a, b) ∈ R if and only if b is greater than or equal to a satisfies the properties of reflexive, antisymmetric, and transitive, but it is not symmetric.

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Answer: area=8cm

Step-by-step explanation:

Answer:

a) Area of shape = 8 square cm.

Step-by-step explanation:

Area of composite shape:

      Area of shape = area of rectangle + 2* area of triangle

         l = 3 cm ; w = 2 cm

\(\sf \boxed{\text{Area of rectangle = l *w}}\)

                             = 3 * 2

                             = 6 cm²

Triangle:

     b = 2 cm

     h = 1 cm

\(\sf \boxed{\text{Area of triangle=$\dfrac{1}{2}*b*h$}}\)

                         \(\sf = \dfrac{1}{2}*2*1\\\\\\ = 1 \ cm^2\)

Area of two triangles = 2 *1

                                    = 2 cm²

Area of shape = 6 + 2

                        = 8 cm²

b) Area of rectangle ABCD = 4 * 2

                                             = 8 cm²

Answer:

750 total people

Step-by-step explanation:

25 to 50 = 1/2

So: 250 x 2 = 500 men

500 + 250 = 750 total

Answer:

D

Sides: a = 7.841   b = 4.369   c = 8

Step-by-step explanation:

Symbols definition of ABC triangle

You have entered side c, angle α, and angle β.

Acute scalene triangle.

Sides: a = 7.841   b = 4.369   c = 8

Area: T = 16.621

Perimeter: p = 20.211

Semiperimeter: s = 10.105

Angle ∠ A = α = 72° = 1.257 rad

Angle ∠ B = β = 32° = 0.559 rad

Angle ∠ C = γ = 76° = 1.326 rad

Height: ha = 4.239

Height: hb = 7.608

Height: hc = 4.155

Median: ma = 5.116

Median: mb = 7.614

Median: mc = 4.928

Inradius: r = 1.645

Circumradius: R = 4.122

Vertex coordinates: A[8; 0] B[0; 0] C[6.65; 4.155]

Centroid: CG[4.883; 1.385]

Coordinates of the circumscribed circle: U[4; 0.997]

Coordinates of the inscribed circle: I[5.736; 1.645]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 108° = 1.257 rad

∠ B' = β' = 148° = 0.559 rad

∠ C' = γ' = 104° = 1.326 rad

Answer:

x - (6/5)x + (8/5x) or

x - (6/5)x + (1.6/x)

Step-by-step explanation:

To divide by 5x, we can use the rules of fraction division:

(5x^2 - 6x + 8) ÷ 5x = 5x^2 ÷ 5x - 6x ÷ 5x + 8 ÷ 5x

Simplifying each term:

= x - (6/5)x + (8/5x)

So the simplified expression is:

x - (6/5)x + (8/5x) or

x - (6/5)x + (1.6/x)

Answer:

B.) -4

Step-by-step explanation:

y=mx+b

b is equal to the y-intercept.

Answer:

-4

Step-by-step explanation:

The slope intercept form is y = mx + b.

m = slope

b = y-intercept

since b = -4, the y-intercept is -4

Answers:

AC = 221.37 feet

BC = 181.34 feet

The values are approximate.

=========================================================

Explanation:

Focus on triangle ACD for now.

The 67 degree angle adjacent to angle D helps us find that angle D = 180-67 = 113 degrees.

Let's find the missing angle C.

A+C+D = 180

55+C+113 = 180

C+168 = 180

C = 180-168

C = 12

Now we can use the Law of Sines to find side d, which is opposite angle D. This is the segment AC.

\(\frac{\sin(C)}{c} = \frac{\sin(D)}{d}\\\\\frac{\sin(12)}{50} = \frac{\sin(113)}{d}\\\\d\sin(12) = 50\sin(113)\\\\d = \frac{50\sin(113)}{\sin(12)}\\\\d \approx 221.369 190\\\\d \approx 221.37\\\\\)

Segment AC is roughly 221.37 feet long.

Keeping our attention on triangle ACD, let's find side 'a'. This is the segment CD.

\(\frac{\sin(C)}{c} = \frac{\sin(A)}{a}\\\\\frac{\sin(12)}{50} = \frac{\sin(55)}{d}\\\\a\sin(12) = 50\sin(55)\\\\a = \frac{50\sin(55)}{\sin(12)}\\\\a \approx 196.995 186\\\\\)

Segment CD is roughly 196.995186 feet long.

----------------------------------------------

Now move onto triangle BCD.

Use the sine ratio to determine side BC.

\(\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\text{D}) = \frac{\text{BC}}{\text{CD}}\\\\\sin(67) \approx \frac{\text{BC}}{196.995186}\\\\\text{BC} \approx 196.995186*\sin(67)\\\\\text{BC} \approx 181.335025\\\\\text{BC} \approx 181.34\\\\\)

Segment BC is roughly 181.34 feet long.

Answer:

See below

Step-by-step explanation:

To find the mean, you take each data point, add them together, and divide it by the number of data points.

Problem 1

Mean of High Temperatures = (65+67+54+52+63+69+75)/7 = 445/7 = between 63 and 64

Problem 2

Mean of Low Temperatures = (61+55+37+29+34+42+54)/7 = 312/7 = between 44 and 45

Answer:

13

Step-by-step explanation:

45 - 6 = 39/3 = 13

Answer:

Forty-five is six more than three times 13.

Step-by-step explanation:

First, you have to set up the equation. We know 45 equals three times a number, 3x, plus 6.

45 = 3x + 6

Subtract 6 from both sides.

39 = 3x

Divide by 3 to isolate the x, and you get 13. Hope that helps!

It is given that the friend agrees to pay half of the total cost of gas for the trip.

It is required to find the amount of money the friend is owing.

To do this, calculate the total cost of gas and evaluate half of it.

The total cost of gas is the sum of the gas charges given:

Calculate half of the total cost:

It follows that the friend is owing $44.

The answer is $44.

When reviewing outliers in a box plot as part of a pre-analysis data screening of participant surveys, the best approach for addressing outliers would be to determine if they are real or data entry errors.

A box plot is a graphical representation of numerical data using quartiles and displays data on the number line. The graph has a box with whiskers extending from either end. Box plots are useful for assessing the spread of data and are used to show the distribution of data based on a five-number summary that includes the minimum and maximum values, the first quartile, the median, and the third quartile.

When reviewing outliers in a box plot as part of a pre-analysis data screening of participant surveys, the best approach for addressing outliers would be to determine if they are real or data entry errors. In a specific context, if they are real, they should be retained and analyzed, but if they are data entry errors, they should be removed because they are not representative of the data set's true nature. The goals of the analysis will determine what approach to use.

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Answer:

144$

Step-by-step explanation:

180/100 = 1.8 subtracted from the price per percent

1.8*20 = 36

180-36 = 144

Answer:

C. QRT and TRQ

\(f(x) = \sqrt{2} + \frac{1}{\sqrt{2} } ( x -1) - \frac{1}{4\sqrt{2} } ( x -1)^{2}\) series about the point x0 for the given function and value of x0.

What is the definition of series in math?

Taylor series of a function f(x)at a point \(x_{0}\) will be defined as -

\(f(x) = f(x_{0} )+ \frac{f'(x_{0}) }{1 !}( x - x_{0}) + \frac{f''(x_{0}) }{2!} ( x - x_{0} )^{2} + \frac{f'''(x_{0}) }{3!} ( x - x_{0} )^{3} + .....................\)

The function we have is -

\(f(x) = \sqrt{2x} and x_{0} = 1\)

Since we need only the first three terms of the taylor series we need to find

\(f(x) = \sqrt{2x}\)

\(f'(x) = \sqrt{2} * \frac{1}{2\sqrt{x} } = \frac{1}{\sqrt2{x} }\)

\(f''(x) = \frac{1}{\sqrt{2} } * \frac{-1}{2x\sqrt{2x} } = - \frac{1}{2\sqrt{2} x\sqrt{x} }\)

putting the value of x = x0 in the above equations we get

   f (1) = \(\sqrt{2}\)

    f''(1) = \(\frac{1}{\sqrt{2} }\)

     f'''(1) = \(\frac{-1}{2\sqrt{2} }\)

putting the values

\(f(x) = f(1) + \frac{f'(1)}{1!}(x -1) + \frac{f''(1)}{2!}(x-1)^{2}\)

\(f(x) = \sqrt{2} + \frac{\frac{1}{\sqrt{2} } }{1} (x- 1) + \frac{\frac{-1}{2\sqrt{2} } }{2} (x - 1 )^{2}\)

\(f(x) = \sqrt{2} + \frac{1}{\sqrt{2} } ( x -1) - \frac{1}{4\sqrt{2} } ( x -1)^{2}\)

The first three terms of taylor series for the given function is given above

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Answer:

3 years

Step-by-step explanation:

We would like to calculate in how much time Rs 1200 will become Rs 1632 at the rate of 12% per annum. Firstly we know that the SI can be calculated by ,

\(\longrightarrow \langle\pink{{\boldsymbol{ SI =\dfrac{Principal \times Rate \times Time }{100}}}}}\rangle\)

Also the total amount is calculated by adding SI and the initial amount ; as ,

\(\longrightarrow \pink{{\boldsymbol{ Amount= Principal + SI }}}\)

Firstly lets find SI as ,

\(\longrightarrow SI = Rs 1632-Rs1200\\ \)

\(\longrightarrow SI = Rs 432 \)

Using the first formula stated above, we have;

\(\longrightarrow Rs 432=\dfrac{(Rs 1200)(12)(t)}{100}\\ \)

\(\longrightarrow t =\dfrac{ 432\times 100}{1200\times 12} yrs \\\)

Simplify,

\(\longrightarrow \boldsymbol{\underline{\underline{{ time = 3\ years }}}} \)

And we are done!

Answer:

Step-by-step explanation:

The tables is completed as follows

5.1.1

1    8

2   16

4    24

6   48

8    64

12    96

5.1.2

The type of proportion is Direct Proportion

5.2.1

1    8

2   4

4    2

6     1

8    0.5

5.1.3

The type of proportion is Inverse Proportion

Direct Proportion: A direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable, and a decrease in one variable results in a proportional decrease in the other variable.

The general formula for a direct proportion is y = kx,

where

k is the constant of proportionality.

Inverse Proportion: An inverse proportion is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable, and a decrease in one variable results in a proportional increase in the other variable.

The general formula for an inverse proportion is y = k/x,

Joint Proportion: A joint proportion is a relationship between three or more variables where one variable is directly proportional to the product of the other variables.

The general formula for a joint proportion is y = kxy,

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Answer:

d=69, e=32, f=79

Step-by-step explanation:

e=32

d=69

f=180-69-32=79

The measure of each of the missing angles include the following:

d = 69.

e = 32.

f = 79.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to the geometric figure, we have the following:

m∠e = 32°

m∠d = 69°

From the linear postulate theorem, we have:

m∠e + m∠d + m∠f = 180°

32° + 69° + m∠f = 180°

m∠f = 180° - (32° + 69°)

m∠f = 79°

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The quotient of (−20/30) ÷ 18/20 given as a simplified fraction is -20/27

Quotient refers to the result obtained by dividing one number by another.

Divisor: This is the number used to divide another number

Dividend: This is the number which is to be divided by another.

(−20/30) ÷ 18/20

= -2/3 ÷ 9/10

= -2/3 × 10/9

= (-2 × 10) / (3 × 9)

= -20/27

Therefore, the quotient of (−20/30) ÷ 18/20 given as a simplified fraction is -20/27

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Answer:

945

Step-by-step explanation:

So the least common multiple of an odd number divided by 7 and 5 is 35

If it's divisible by 9, the least common multiple is 35 times 9, which is 315

And since it's odd and it's greater than 700,

So 315 times 3 is 945, which satisfies 9 in the hundreds place, and 35 times 27 is 945, which satisfies a multiple of 27

Answer:

The measure of ∠CAD is 69°

Step-by-step explanation:

In ΔABC

∵ D is the mid-point of AB

∵ E is the mid-point of BC

∴ DE is parallel to AC

→ From parallelism

∵ DE // AC

∴ m∠EDB = m∠CAD → corresponding angles

∵ m∠EDB = 83 - 7x

∵ m∠CAD = 7x + 55

→ Equate them

∴ 7x + 55 = 83 - 7x

→ Add 7x to both sides

∵ 7x + 7x + 55 = 83 - 7x + 7x

∴ 14x + 55 = 83

→ Subtract 55 from both sides

∵ 14x + 55 - 55 = 83 - 55

∴ 14x = 28

→ Divide both sides by 14

∴ x = 2

→ To find m∠CAD, substitute x by 2 in its measure

∵ m∠CAD = 7(2) + 55

∴ m∠CAD = 14 + 55

∴ m∠CAD = 69°

∴ The measure of ∠CAD is 69°

Answer:

\((\frac{12}{-4n^{2}})\)

Step-by-step explanation:

\((\frac{3}{-2n})(\frac{4}{2n})=(\frac{3*4}{-2n*2n})=(\frac{12}{-4n^{2}})\)

Answer:

\( -\dfrac{3}{n^2} \)

Step-by-step explanation:

\( \dfrac{3}{-2n} \times \dfrac{4}{+2n} = \)

\( = \dfrac{3 \times 4}{-2n \times 2n} \)

\( = \dfrac{12}{-4n^2} \)

\( = -\dfrac{3}{n^2} \)

Answer:

Step-by-step explanation:

=the highest common factor is \(3b^{3}\)

therefore you can divide each and every term of the expression and take it out of the brackets.

\(=3b^{3} (3+8)\\=3bx^{3} (11)\)

Although I still see no use of factorising because there are only like times that is what I put on table. Please ask if you have questions

The probability of taking either a math class or a science class P(G ∪ H) is 0.14.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.  

To find the probability of taking either a math class or a science class (G ∪ H), we can use the inclusion-exclusion principle:

P(G ∪ H) = P(G) + P(H) - P(Gn H)

Given:

P(G) = 0.25

P(H) = 0.28

P(Gn H) = 0.39

Substituting these values into the formula:

P(G ∪ H) = 0.25 + 0.28 - 0.39

= 0.53 - 0.39

= 0.14

Therefore, P(Gu H) (the probability of taking either a math class or a science class) is 0.14.

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Completely factored expressions are:

1. x² - 7x - 18 can be factored as:

(x - 9)(x + 2)

Expand the expression using FOIL:

(x - 9)(x + 2) = x² + 2x - 9x - 18 = x² - 7x - 18

2. p² - 5p - 14 can be factored as:

(p - 7)(p + 2)

Expand the expression using FOIL:

(p - 7)(p + 2) = p² + 2p - 7p - 14 = p² - 5p - 14

3. m² - 9m + 8 can be factored as:

(m - 1)(m - 8)

Expand the expression using FOIL:

(m - 1)(m - 8) = m² - 8m - m + 8 = m² - 9m + 8

Therefore, the completely factored expressions are:

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